Question

Consider the postfix expression: a-b c*(d*e-f)/(g h*k). The equivalent postfix (reverse polish notation) expression is:

1) ab-c de*f-gh k**/
2) ab-cde*f-* ghk* /
3) abc -e*f-* ghk* /
4) none of these

Answer 1

To convert the infix expression to postfix expression, move each operator after its operands. The correct postfix expression for a-b c*(d*e-f)/(g h*k) is ab-cde*f-*ghk*/.

Step-by-step explanation:

The question refers to the conversion of an infix expression to a postfix expression, which is a part of Mathematics, specifically in the area of algebra and computer science where such notations are commonly used. To convert the given infix expression a-b c*(d*e-f)/(g h*k) into postfix notation, we must follow the order of operations while moving each operator after its operands as required by postfix notation.

To solve this, we can use a step-by-step approach:

1. Identify the innermost parentheses: (d*e-f) and (g h*k)
2. Convert them to postfix: de*f- and ghk*
3. Replace each in the original expression: a-b c*de*f-/ghk*
4. Apply postfix conversion to remaining parts: a b- c * and /
5. Combine the converted parts: ab-cde*f-*ghk*/

The correct postfix expression is therefore ab-cde*f-*ghk*/, which matches option 2 in the question. Note that the asterisks indicate multiplication, and the slashes indicate division in postfix notation.